minimaxväärtused

Minimaxväärtused, often translated as minimax values, are a fundamental concept in game theory and artificial intelligence, particularly in the context of zero-sum games. These values represent the best possible outcome a player can guarantee for themselves, assuming their opponent plays optimally to counter them. The minimax algorithm is designed to find these values by exploring the game tree, which represents all possible moves and counter-moves.

In a two-player, zero-sum game, one player's gain is precisely the other player's loss. The minimax algorithm operates by looking ahead to future game states. For the player whose turn it is to maximize their score (often called the maximizer), they will choose a move that leads to the state with the highest possible minimax value. Conversely, the player whose turn it is to minimize the maximizer's score (the minimizer) will choose a move that leads to the state with the lowest possible minimax value.

The algorithm recursively explores the game tree. At terminal nodes (game end states), the value is the actual score. For non-terminal nodes, the maximizer chooses the maximum of the values of its children, while the minimizer chooses the minimum. This process continues until the root of the tree is reached, revealing the optimal strategy and the guaranteed outcome for each player if they both play perfectly. The minimax value for a given position is the value that the maximizer can achieve, regardless of the minimizer's moves.